It wouldn't take every New Yorker filing suits to cause a massive headache for Tony. Knowing human nature, some would be bound to sue. If even a few major property owners laid claims for damages Tony could be tied up in litigation with heavy costs for legal fees. There would be insurance on the property, of course, but any insurer worth its salt would find a way to avoid paying out, leaving Stark with the financial burden. Black probably won't go with that, but if he did it could be part of The Mandarin's plot to destroy Tony.

Senator Whatsisface was making noises at the end of the movie about holding the team responsible for what happened. We've all seen how senate and congressional hearings can be used IRL to gin up all manner of problems for corporations. They had already been after Tony to give up the Iron Man armor before. Even though the Air Force has War Machine, they don't have Stark's schematics or his manufacturing process. The invasion could give the government another excuse to try and seize the whole shebang, once and for all.

They want to mass produce his suit and make an army of Ironmen.

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What is the most indestructable thing in the avengers? Ironman's suit, Captain America's Shield, or Thor's Hammer?﻿ The correct answer is Hulk's Pants